Finite Group DatabasebetaFinite Group Databasebeta| order | 5820 |
| automorphism | Aut(G) order 2234880 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2910 |
| direct product | C2×D1455 |
| unambiguous semidirect product | (C2×C3)⋊D485 |
| unambiguous semidirect product | (C2×C5)⋊D291 |
| unambiguous semidirect product | (C2×C97)⋊D15 |
| Fitting, socle | C2×C3×C5×C97 ⋊ C2 |
| derived, Hall | C3×C5×C97 ⋊ C22 |
| Hall | C5×C97 ⋊ C2×D3 |
| Hall | C3×C97 ⋊ C2×D5 |
| Sylow | C97 ⋊ C2×D15 |
| Hall | C3×C5 ⋊ C2×D97 |
| Sylow | C5 ⋊ C2×D291 |
| Sylow | C3 ⋊ C2×D485 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1455 |
| commutator, hypocenter | C3×C5×C97 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C97 | C2 |
| LCS | G ▷ C3×C5×C97 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
1458 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4365, C2×C3⋊(C5⋊(D97⋊C3)), D3×D1455, … |
| maximal normal subgroup of | C2×C3⋊(C5⋊(D97⋊C3)), C2×C3×D1455, C2×C5×D1455, … |
| maximal quotient of | C2×D4365, D3×D1455, C2×C3⋊D1455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5820, 52);